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This study presents a general alternative scheme of the procedure and necessary conditions for solving the $n$-body problem. The presented solution is not a solution of the classical problem, where the initial conditions of positions and…
Decision-theoretic troubleshooting is one of the areas to which Bayesian networks can be applied. Given a probabilistic model of a malfunctioning man-made device, the task is to construct a repair strategy with minimal expected cost. The…
Deep Convolutional Neural Networks (DCNN) have been proven to be effective for various computer vision problems. In this work, we demonstrate its effectiveness on a continuous object orientation estimation task, which requires prediction of…
This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…
We are concerned with the numerical solution of a class integro-differential equations, known as Neural Field Equations, which describe the large-scale dynamics of spatially structured networks of neurons. These equations have many…
Why would anyone wish to generalize the already unappetizing subject of rigid body motion to an arbitrary number of dimensions? At first sight, the subject seems to be both repellent and superfluous. The author will try to argue that an…
In many real-world settings, image observations of freely rotating 3D rigid bodies may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of classical estimation…
Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…
Designing mechanically efficient geometry for architectural structures like shells, towers, and bridges, is an expensive iterative process. Existing techniques for solving such inverse problems rely on traditional optimization methods,…
Many complex physical systems admit natural decomposition into an exactly solvable component and a perturbative correction. Rather than training neural networks to learn complete trajectories from scratch, we introduce Neural Network…
In this paper, we consider the elliptic collinear solutions of the classical $n$-body problem, where the $n$ bodies always stay on a straight line, and each of them moves on its own elliptic orbit with the same eccentricity. Such a motion…
The elliptic restricted three body problem has been well studied. However, the previous formulations of the problem have used a rotating coordinate system to keep the positions of the primary and secondary on the x-axis. This requires the…
We use machine learning techniques to solve the nuclear two-body bound state problem, the deuteron. We use a minimal one-layer, feed-forward neural network to represent the deuteron S- and D-state wavefunction in momentum space, and solve…
We study the problem of minimal resistance for a body moving with constant velocity in a rarefied medium of chaotically moving point particles, in Euclidean space R^d. The particles distribution over velocities is radially symmetric. Under…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…
Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations.…
Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should…
Exact analytic solutions are obtained in three-body problem for the scattering of light particle on two fixed centers in the case when pair potentials have a separable form. Solutions show an appearance of new three-body resonance states…
Identification of defects or anomalies in 3D objects is a crucial task to ensure correct functionality. In this work, we combine Bayesian learning with recent developments in quantum and quantum-inspired machine learning, specifically…
Given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, we show how to construct a new solution of the constraints which is itself asymptotically Euclidean, and which contains…